Question

Represente os décimas infinitos períodicos em fração
a) 0,666...
b)0,242424...
c)0, 234234234...
d)0,5555...

2- Transforme os décimas infinitos períodicos em fração

a) 0,211111...
b)0,13333...
c)0,24666...
me ajudem prfv​

Answer 1

Explicação passo-a-passo:

1)

a)

x = 0,666...

10x = 6,666...

10x - x = 6,666... - 0,666...

9x = 6

x = 6/9

x = 2/3

b)

x = 0,242424...

100x = 24,242424...

100x - x = 24,242424... - 0,242424...

99x = 24

x = 24/99

x = 8/33

c)

x = 0,234234234...

1000x = 234,234234...

1000x - x = 234,234234... - 0,234234...

999x = 234

x = 234/999

x = 26/111

d)

x = 0,555...

10x = 5,555...

10x - x = 5,555... - 0,555...

9x = 5

x = 5/9

2)

a)

10x = 2,111...

100x = 21,111...

100x - 10x = 21,111... - 2,111...

90x = 19

x = 19/90

b)

10x = 1,3333...

100x = 13,333...

100x - 10x = 13,333... - 1,333...

90x = 12

x = 12/90

x = 4/30

c)

100x = 24,666...

1000x = 246,666...

1000x - 100x z= 246,666... - 24,666...

900x = 222

x = 222/900

x = 74/300